make_acf_psd: Transforms Estimated Autocorrelation Functions into Positive...
In robts: Robust Time Series Analysis

Description Usage Arguments Details Value Author(s) References See Also

Transforms acf estimations into positive semidefinite ones by iterative projections. See Dürre et al. (2015) for details.

This function is intended for internal use and is called by the function acfrob.

1	make_acf_psd(acfvalues, ...)

`acfvalues`	numeric vector with original acf estimation at lags 1,2,...
`...`	tuning parameters for internal functions, see Details.

The function transforms a vector into a semidefinite one by the projection algorithm described in Al-Homidan (2006). First, based on the estimated acf, the corresponding correlation matrix (of the lagged time series) is build. Then the best positive semidefinite matrix with Toeplitz structure is computed by iteratively projecting onto positive semidefinite and Toeplitz matrices. The algorithm stops either a maximal number of iterations is reached maxit = 100 or the changes of the Frobenius norm is smaller then a given threshold tol = 10^(-8), both values can be changed by the ... argument. See Dürre (2015) for more details on the algorithm.

Numeric vector of transformed autocorrelations.

Alexander Dürre, Tobias Liboschik and Jonathan Rathjens

Al-Homidan, S.: (2006): Semidefinite and second-order cone optimization approach for the toeplitz matrix approximation problem, Journal of Numerical Mathematics, vol. 14, 1–15, doi: 10.1515/156939506776382148.

Dürre, A., Fried, R. and Liboschik, T. (2015): Robust estimation of (partial) autocorrelation, Wiley Interdisciplinary Reviews: Computational Statistics, vol. 7, 205–222, doi: 10.1002/wics.1351.

The function acfrob for robust estimation of the autocorrelation function.

robts documentation built on May 2, 2019, 4:55 p.m.